1. Quantum Hall Ferromagnets-II Ramin Abolfath Luis Brey Anton Burkov Rene Cote Jim Eisenstein Herb Fertig Steve Girvin Charles Hanna Tomas Jungwirth Kentaro Nomura Leo Radzihovksy (Doug) Rajaraman Mark Rasolt Jairo Sinova Kun Yang Les Houches June 2006 University of Texas at Austin

2. Skyrmions

3. Skrymion in 2D O(3) Ferromagnet

4. QHF Energy Functional Landau Gauge Energy Functional Exchange Interaction Form Factor

5. Quantum Hall Skyrmions Carry Charge !! Sondhi et al. PRB ‘93

6. Skyrmions in Ground State- II Hartree-Fock Skyrmion WF Symmetric Gauge LLL Wavefunctions Classical # of reversed spins

7. Skyrmions Size n=0 LL Fertig et al. PRB ’94 ‘97 K g

8. Fertig et al. PRB ’94 Barrett & Tycko PRL ‘95 Skyrmions in Ground State

9. Skyrmion Crystal Brey et al. PRL ‘95

10. Cote et al. PRL ‘97 Skyrmion Crystal Collective Excitations k 1.5 ~ phonons k 1 ~ new Larmour

11. QHF Graphene Nomura cond-mat/06 – Alicea cond-mat/06 – Yang cond-mat/06

12. Graphene Landau Levels Conduction Valence Semenoff Haldane Kane Mele

13. Graphene Quantum Hall Effect Novoselov et al. – Manchester – Nature (2005)  xx  xy n

14. Zhang et al. – Columbia – cond-mat/0602649 B= 45 Tesla

15. SU(4) Ferromagnetism Arovas/Karlhede (1999) – Ezawa (2002)  A(E) Landau Band Exchange Integral

16. QHF Stoner Criterion Fogler & Shklovskii (1995); Maude et al. (2005) AX > 1  QHF Landau Band Width Interaction Energy Scale

17. Zero Field Conductivity   V gate Geim Nature (2005) Golden Rule ?

18. Coulomb Scattering I where 2-3

19. Coulomb Scattering II 

20. Self-consistent Screening Das Sarma Ando Screened Exchange

21. Phase Diagram Manchester   1.5 Columbia   5.0 Nomura cond-mat/0603 PRL

22. Broken Symmetry SU(N)/(SU(M) x SU(N-M)) coset space 2 (N-M) parameters

23. Graphene Skyrmions - I Graphne Form Factor Yang et al., cond-mat/0605666

24. Graphene Skyrmions – II SU(N)/(SU(M-1) x SU(N-M-1)) coset space 2 (N-M) + 2 (N-1) parameters Skyrm Lattice has N Goldstone modes k 1.5 & 2 k 1 & k 2

25. Next Time: Skyrmions QHF Anistropy – Ising or XY QHF in Graphene Quantum Hall Superfluids & Pseudo-spin Transfer Torques